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Articles 1 - 16 of 16
Full-Text Articles in Physics
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
All HMC Faculty Publications and Research
The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …
Posterminaries: More Or Less Modern, Alexander H. King
Posterminaries: More Or Less Modern, Alexander H. King
Alexander H. King
It is yet another sign that I am aging. More and more often when young researchers hand me a written report of their research, I find myself criticizing their introductory section: “You need to start your literature survey with the original papers on this topic. Go and read…” followed by a citation to some classic of the learned literature.
Control Of Porosity In Fluoride Thin Films Prepared By Vapor Deposition, Alexander H. King
Control Of Porosity In Fluoride Thin Films Prepared By Vapor Deposition, Alexander H. King
Alexander H. King
We have measured the porosity in thin films of lithium fluoride (LiF), magnesium fluoride (MgF2), barium fluoride (BaF2), and calcium fluoride (CaF2) as a function of the substrate temperature for films deposited by thermal evaporation onto glass substrates. The amount of porosity in the thin films was measured using an atomic force microscope and a quartz crystal thickness monitor. The porosity was very sensitive to the substrate temperature and decreased as the substrate temperature increased. Consistent behavior was observed among all of the materials in this study.
Posterminaries: Full Circle, Alexander H. King
Posterminaries: Full Circle, Alexander H. King
Alexander H. King
A few years ago, I was walking near the old Union Station in Pittsburgh with a colleague only slightly younger than myself, when we happened upon some large-scale relics of the steel industry displayed for public viewing. “You don’t see too many of those in public parking lots,” I offered. “Um… what is it?” was the response. I suppose I was just a little surprised that a prominent materials scientist did not recognize a Bessemer converter—arguably the principal source of wealth during the U.S. industrial revolution—but this conversation took place back when steel was in decline, and many university Materials …
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …
An Isotropic Metric, Joseph D. Rudmin
An Isotropic Metric, Joseph D. Rudmin
Virginia Journal of Science
An isotropic metric for a black hole and a better vacuum condition \nabla^2 V_G =0 are presented which yield distinct terms for the energy densities of ordinary matter and gravitational fields in the Einstein tensor (G^44 =-g^2 (2\nabla^2 V_G +(\nabla V_G)^2)). This model resolves an inconsistency between electromagnetism and gravity in the calculation of field energy. Resolution of this inconsistency suggests a slight modification of the Einstein equation to gG^\mu\nu = 8\pi G T^\mu\nu.
Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun
Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun
Xiao-Jun Yang
The dynamic feature of high buildings is discussed in the present study with the application of ANSYS，the large finite element analysis software，aimed at the analysis of dynamic response of high buildings．Based on the case of a 15一story-building，a model of beam and shell 3-D finite element structure is built and the frequency of structure and the mode of vibration are computed in the study；furthermore，the structural dynamic response is discussed under different seismic waves with the use of the history analysis method．The results show that the more intense the seismic wave is，the bigger is the dynamic response of the buildings．The information can …
Thermal Effects On Mechanical Grinding-Induced Surface Texture In Tetragonal Piezoelectrics, Wonyoung Chang, Alexander H. King, Keith J. Bowman
Thermal Effects On Mechanical Grinding-Induced Surface Texture In Tetragonal Piezoelectrics, Wonyoung Chang, Alexander H. King, Keith J. Bowman
Alexander H. King
The effect of temperature on grinding-induced texture in tetragonal lead zirconate titanate (PZT) and lead titanate (PT) has been investigated using in situ x-ray diffraction (XRD) with an area detector. In contrast with previous results on electrical poling, mechanically-ground PT and soft PZT materials retain strong ferroelastic textures during thermal cycling, even after excursions to temperatures slightly above the Curie temperature. The relationship between the residual stresses in the surface region, caused by grinding, and those resulting from domain wall motion is elucidated by in situ texture measurements obtained during thermal cycling.
How Surface Stresses Lead To Size-Dependent Mechanics Of Tensile Deformation In Nanowires, M. Ravi Shankar, Alexander H. King
How Surface Stresses Lead To Size-Dependent Mechanics Of Tensile Deformation In Nanowires, M. Ravi Shankar, Alexander H. King
Alexander H. King
It has been proposed that surface and interface stresses can modify the elastic behavior in nanomaterials such as nanowires. The authors show that surface stresses modify the tensile response of nanowires only when nonlinear elastic effects become important leading to cross terms between the applied stress and the surface stress. These effects are only significant when the radius of the nanowire is of the order of a few nanometers. The resulting alteration of tensile stiffness, though effected in part by the nonlinear elastic modulus, is particularly wrought by a modification of the stress state in the deformed nanowire.
Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge
Diffusion And Fractional Diffusion Based Models For Multiple Light Scattering And Image Analysis, Jonathan Blackledge
Articles
This paper considers a fractional light diffusion model as an approach to characterizing the case when intermediate scattering processes are present, i.e. the scattering regime is neither strong nor weak. In order to introduce the basis for this approach, we revisit the elements of formal scattering theory and the classical diffusion problem in terms of solutions to the inhomogeneous wave and diffusion equations respectively. We then address the significance of these equations in terms of a random walk model for multiple scattering. This leads to the proposition of a fractional diffusion equation for modelling intermediate strength scattering that is based …
Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian
Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian
Mechanical Engineering Faculty Research
RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …
Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert
Articles
This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …
Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant
Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant
Tim Marchant
The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological self-heating is present. The heat release rate due to biological activity is modelled by a function which is a monotonic increasing function of temperature over the range 0⩽T⩽a, whilst for T⩾a it is a monotone decreasing function of temperature. This functional dependence represents the fact that micro-organisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1-d slab and 2-d rectangular slab geometries. In both cases there are two generic steady-state …
Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higher-order version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed. …
Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant
Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant
Tim Marchant
The collision of solitary waves for a higher-order modified Korteweg-de Vries (mKdV) equation is examined. In particular, the collision between solitary waves with sech-type and algebraic (which only exist on a non-zero mean level) profiles is considered. An asymptotic transformation, valid if the higher-order coefficients satisfy a certain algebraic relationship, is used to transform the higher-order mKdV equation to an integrable member of the mKdV hierarchy. The transformation is used to show that the higher-order collision is asymptotically elastic and to derive the higher-order phase shifts. Numerical simulations of both elastic and inelastic collisions are performed. For the example covered …
Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant
Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant
Tim Marchant
Wool scouring is the process of washing dirty wool after shearing. Our model numerically simulates contaminant movement in a wool scour bowl using the advection–dispersion equation. This is the first wool scour model to give time-dependent results and to model the transport of contaminants within a single scour bowl. Our aim is to gain a better understanding of the operating parameters that will produce efficient scouring. Investigating the effects of varying the parameters reveals simple, interesting relationships that give insight into the dynamics of a scour bowl.